If the "Z" angle isn't matched close enough, the drive shaft will shake/vibrate/etc. What happens is that the end U-Joints get slightly out of phase and wear that way to become more and more prone to vibrate/shake
Betcha the tranny's rear mount has too much compliance and allows the "Z" angle to move around and once it starts to vibrate/shake/etc...it will continue until slowed down.
Also, 2 piece drive shafts with a center bearing/bushing has been known to have this on occasion after many miles have worn the center bearing/carrier